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On the mean-field limit for the consensus-based optimization

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arxiv 2105.12919 v1 pith:ASXS6YMB submitted 2021-05-27 math.OC math.APmath.DS

Hui Huang , Jinniao Qiu This is my paper · ORCID
classification math.OCmath.APmath.DS
keywords limitoptimizationparticleconsensus-basedmean-fieldadaptargumentassociated
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abstract

This paper is concerned with the large particle limit for the consensus-based optimization (CBO), which was postulated in the pioneering works [6,28]. In order to solve this open problem, we adapt a compactness argument by first proving the tightness of the empirical measures $\{\mu^N\}_{N\geq 2}$ associated to the particle system and then verifying that the limit measure $\mu$ is the unique weak solution to the mean-field CBO equation. Such results are extended to the model of particle swarm optimization (PSO).

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  1. Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games

    math.OC 2025-05 conditional novelty 5.0 of 10

    This paper establishes existence, uniqueness, and a finite-particle mean-field error rate of order N^{-γ} for a multi-species consensus-based algorithm for multiplayer Nash games.

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